Modify default settings for subdivision surface modifier
The video you linked to is a tutorial for the Sensei addon, which is a free addon that you can download and try. You will notice that the Sensei addon replaces a lot of the blender UI so that it's own operators are used, which is how the various defaults are different than blender's defaults.

Like the Sensei addon, you can create your own addon/s that perform tasks with your settings. You can start by creating an addon that defines an operator which adds a subsurf modifier with settings you want as well as turning on the draw wire settings for the object. This can be then be added to existing menus or custom hotkeys. To learn to create addons start with a Python tutorial if you don't know Python yet, then go through blender's addon tutorial.

Some code to put into your operators execute() method could be something like -

# bpy.context.active_object is needed if you test this script
# inside an operators execute you only want context.active_object
obj = bpy.context.active_object
# objects draw wireframe settings
obj.show_wire = True
obj.show_all_edges = True
# add a subsurf modifier
m = obj.modifiers.new('Subsurf', 'SUBSURF')
# this turns on optimal display
m.show_only_control_edges = True
# this shows the edit mode vertices on the
# deformed mesh not the real vertices
m.show_in_editmode = True
m.show_on_cage = True